Aperiodic (resistive) speaker enclosure with quadric surfaces

• Loudspeaker enclosure with aperiodic (resistive) vent to avoid harmful resonance of insufficient air volume.
• Inner surface consists of two types of quadric surfaces (parabola and ellipse) that share common locus.
• Aperiodic vent can be tuned easily by screwing out the cap. The cap can be replaced by sealed (closed) cap or bass-reflex ports to compare sounds.

Design

Parabola collects parallel rays to a locus, and ellipse leads the ray from a locus to the other
. Therefore I arranged two objects so that those loci coincide. Speaker unit is placed at the left end, and sound absorption material and aperiodic vent is placed at the other side.

The condition of ray concentration is not broken by rotation around the locus, so I arranged two primitives to place the speaker unit at the bottom, and reduces the depth of the speaker.

Regarding the long wavelength of the sound wave (around 5cm - 10m), the theory of reflection described above is not applicable. Therefore the shape of this speaker is just for fun or scientific flavor.

The air volume of this speaker is too small to suppress Q value (mathematical index of resonance quality), so I used aperiodic vent (resistive port) design. The space between the cap (green) and inner grill (blue) is filled by batting which gives resistance to the air velocity. It much reduces the Q value of the speaker with less air volume.

Needle at the locus can be used to fix additional air absorbing material. In general, sound absorption efficiency increases when you place the material at the middle of the speaker (if you stick the material at the inner surface, the effect of sound absorption is limited).

The shape of the stand (red) is hyperbola which locus is placed at the other primitives. Therefore this speaker has three representative quadrics, parabola, ellipse ad hyperbola.

Air volume in the enclosure works as a spring to strengthen the vibration of the cone. The smaller volume causes stronger resonance. Air mass in the bass reflex port blocks the leakage of air pressure at the higher resonance frequency. In both sealed and bass-reflex designs, there is no energy-absorption component. In contrast, aperiodic design has a resistive element to absorb the energy of resonance, and tight and clear sound can be achieved even if the air volume is limited.

You can adjust the amount of batting by measuring the impedance curve. If the speaker is well tuned, peak of impedance (which is related to the Q value of resonance) is much reduced from not only the closed enclosure but also the bare speaker unit (and infinity baffle plate speaker condition). It realizes tight and high definition sound with small enclosure.

With this insufficient air volume in the enclosure, it is difficult to control the resonance of the cone and air spring when we use ordinary sealed(closed) or bass-reflex designs. As shown in the figure above, this speaker has a resonance peak around 300Hz and it should be suppressed. Sealed enclose (green) has a certain peak. Bass reflex design (two blue curves) does not solve the problem, and bass emphasis effect is also very limited. In contrast, aperiodic design (red) well maintains the resonance peak, and the SPL curve can be flatten.

Black curve is the response without cap.

Category: Audio